Timeline for Concentration inequality for the sample covariance matrix
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 12, 2021 at 16:24 | comment | added | Uzu Lim | I see. Currently I cannot see how that would help me prove a desired concentration inequality, could you tell me how? One expression I know for $\hat \Sigma_2$ is obtained by expanding the sample mean part, which gives $\hat \Sigma_2 = \frac1m \sum_i x_i x_i^\top - \frac1{m(m-1)} \sum_{i \neq j} x_i x_j^\top$. I wonder if this is one of the expressions you consider as relevant. | |
| Apr 12, 2021 at 16:11 | comment | added | whuber♦ | The point is that there are algebraically equivalent expressions for $\hat\Sigma_2$ that do not use the sample mean at all. | |
| Apr 12, 2021 at 15:18 | comment | added | Uzu Lim | The expression $\hat \Sigma_1$ uses the true mean and the expression $\hat \Sigma_2$ uses the sample mean. I'm trying to obtain a concentration inequality for $\hat \Sigma_2$. | |
| Apr 12, 2021 at 15:09 | comment | added | whuber♦ | The covariance matrix can be defined without referring to the mean. See stats.stackexchange.com/a/18200/919 for a description of one way. (You will easily see how this visual explanation translates to a mathematical formula.) | |
| Apr 12, 2021 at 14:58 | history | asked | Uzu Lim | CC BY-SA 4.0 |